lpmn(m, n, z)[source]¶
Sequence of associated Legendre functions of the first kind.
Computes the associated Legendre function of the first kind of order m and degree n,
Pmn(z)= \(P_n^m(z)\), and its derivative,
Pmn'(z). Returns two arrays of size
Pmn'(z)for all orders from
0..mand degrees from
This function takes a real argument
z. For complex arguments
zuse clpmn instead.
m : int
|m| <= n; the order of the Legendre function.
n : int
n >= 0; the degree of the Legendre function. Often called
l(lower case L) in descriptions of the associated Legendre function
z : float
Pmn_z : (m+1, n+1) array
Values for all orders 0..m and degrees 0..n
Pmn_d_z : (m+1, n+1) array
Derivatives for all orders 0..m and degrees 0..n
- associated Legendre functions of the first kind for complex z
In the interval (-1, 1), Ferrer’s function of the first kind is returned. The phase convention used for the intervals (1, inf) and (-inf, -1) is such that the result is always real.
[R484] Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html [R485] NIST Digital Library of Mathematical Functions http://dlmf.nist.gov/14.3